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Newton's First Law
Forces and Motion
Inertia and Newton's first law
for 14-16
Inertia is a powerful idea. Using many examples will help students to understand what it means.
Demonstration
The tendency of a body to resist acceleration is called its inertia. This experiment provides direct experience of applying force and experiencing inertia.
Apparatus and Materials
- Tin cans, large, 2
- Sand
- String
Health & Safety and Technical Notes
A ladder or step-ladder must be used when attaching strings to a ceiling beam. A ladder must be steadied by a second adult. If it is necessary to stand more than two metres from the floor, the worker must have been trained for work at height.
Ensure that students use this apparatus in a manner that creates no hazard for themselves or for others.
Read our standard health & safety guidance
The string should be strong enough to support the load safely.
Procedure
- Fill one can with sand and leave the other one empty. Hang them both by long strings.
- Give each of them a short, sharp push. Compare how easy it is to accelerate them.
- Allow the pendulums to swing and push them in a direction roughly perpendicular to their motions. This produces acceleration in a different direction from the motion, and the cans change direction. Again, the two cans do not experience the same accelerations.
- Try to stop swinging pendulums. Compare the changes in motion of the cans when you exert similar forces on them.
Teaching Notes
- Do this as a participative demonstration. Ask your students to move the masses.
- There is no question of friction causing a difference in this case because the cans are the same size and shape.
- This simple activity makes fundamental points about force and related quantities. The points are relevant both at introductory and at advanced levels, and can be summarized as:
- Force, when it is not ‘balanced’ by other forces, is what produces change in motion (acceleration)
- Mass is what resists change in motion (acceleration).
- Thus, all in one go, you have working definitions of both force and inertial mass. (There is an additional ‘parallel’ definition of mass: Gravitational mass is what allows a body to exert and experience gravitational force. To see how the two definitions of mass relate to each other you would have to consider Einstein’s theory of general relativity.)
- Emphasize that it is not just the
start
of motion that is resisted by masses, butany
change in motion, including slowing down and stopping, or changing direction. - The activity provides a suitable introduction to Newton’s first law.
- You could fire ping-pong balls or peas at the cans as a way of comparing the responses of cans with different mass.
- You could discuss seat belts in cars. Some are called inertia reel belts.
This experiment was safety-tested in March 2005
Up next
Inertia on a low friction surface
Class practical
This seemingly simple activity makes fundamental points about force and related quantities.
Apparatus and Materials
- Smooth surface with frame, e.g. mounted glass plate
- Mass, 1 kg
- Mass, 0.5 kg
- Gas jar lid
- Steel ball bearings, small, to to 2,000
Health & Safety and Technical Notes
It would be best to avoid using polystyrene beads as an alternative to ball bearings. These are now classified as a dangerous substance because of the pressure generated when they expand.
If the glass plate is one metre square, it will require two persons to lift it onto the bench.
Ensure that the beads are not scattered on the floor.
Read our standard health & safety guidance
A mounted glass plate provides a low friction surface, but other materials will serve. The surface must have a frame to contain the ball bearings. (Strictly these are the balls used to make ball bearings.
The number of ball bearings required depends on the size of the surface. There should be enough to spread quite thinly on the surface, so that the mass on the gas jar lid can move with little frictional resistance.
The ball bearings should be about 2 mm in diameter.
Procedure
- Make a layer of ball bearings quite thinly spread on the flat surface, to reduce the frictional forces.
- Stand the 0.5 kg mass on the gas jar lid and rest it on the ball bearings. A little blu-tack may help it to stick.
- Push the mass gently.
- Push the mass harder and note the difference in behaviour.
- Replace the 0.5 kg mass with the 1.0 kg mass. Repeat the actions and note the differences in how it feels and how it behaves.
- Try pushes on moving masses.
Teaching Notes
- Do this as a participative demonstration. Ask your students to move the masses.
- This simple activity makes fundamental points about force and related quantities. The points are relevant both at introductory and at advanced levels, and can be summarized as:
- Force, when it is not
balanced
by other forces, is what produces change in motion (acceleration) - Mass is what resists change in motion (acceleration)
- The tendency of a body to resist acceleration is called its inertia.
- Thus, all in one go, you have working definitions of both force and inertial mass. (There is an additional
parallel
definition of mass: Gravitational mass is what allows a body to exert and experience gravitational force. To see how the two definitions of mass relate to each other you would have to consider Einstein's theory of general relativity.) - Emphasize that it is not just the
start
of motion that is resisted by masses, butany
change in motion, including slowing down and stopping, or changing direction. - The activity provides a suitable introduction to Newton's first law.
This experiment was safety-tested in March 2005
Up next
The inertia balance or 'wig-wag'
Class practical
This activity shows that resistance to motion depends on the mass of the body being accelerated, rather than on its weight.
Apparatus and Materials
For each student group
- Inertia balance
- Masses
- G-clamps
- Elastic band
Health & Safety and Technical Notes
If using hack-saw blades, take care to avoid cuts or scratches.
Do not overload the system, or the blades might buckle or snap. Test this safely before the lesson, and make sure that students cannot add an excessive load.
Take care when masses fall to the floor. Use a box or tray lined with bubble wrap (or similar) under heavy objects being lifted. This will prevent toes or fingers from being in the danger zone.
Read our standard health & safety guidance
You can purchase wig-wags, but it is cheaper and not too difficult to make them. Use two hack-saw blades or equivalent lengths of metal strip, and place a block of wood between them at one end. This serves as anchorage to be fixed to the table. Place another block of wood between them at the other end, to act as the platform which carries the loads.
It is essential to clamp each blade very firmly on both sides of the blocks of wood. Place another small block of wood or metal outside the blade, flush with the main block, so that the blade emerges as if from the well-matched jaws of a vice. Then drive screws through the small blocks, through holes in the saw blades, and into the big block.
For a temporary balance, use a large G-clamp to clamp small blocks, both blades, and the large block together, in a multiple sandwich with a similar clamp at the other end.
Cylindrical masses held in holes in the vibrating platform work well with this experiment, but are not essential (see illustrations below).
Procedure
- Clamp one end of the wig-wag rigidly to a lab bench with G-clamps so that the blades stick out horizontally. The other end acts as a platform that can vibrate to and fro.
- Pull the platform to one side, release it, and watch it vibrating.
- Increase the load by adding masses to the platform. Use an elastic band to secure the loads. Note the change in resistance to motion (inertia) and in the vibration time (period of the motion).
- Support the load vertically with a thread holding most of its weight, leaving only a little of it supported by the moving platform. The moving platform will still carry the full mass of the load in horizontal motion. With a bit of practice, you can do this by pulling upward on a taut thread and moving your hand to and fro in time with the motion of the platform. Or you can fix the thread to a support as far as possible above the platform. You have changed the vertical force.
- Find out whether this makes a difference to the wig-wag motion.
Teaching Notes
- The oscillation of the system does not depend on the pull of the Earth. The period of oscillation, T , depends only on the mass, m , of the oscillating body, not its weight. T ∝√ m .
- If the system is suitably calibrated, the period of oscillation can be used to determine an unknown mass.
- This is the principle employed in machines which measure mass in Space.
This experiment was safety-tested in August 2007
Up next
More inertia experiments
Demonstration
These are short activities, suitable for demonstration as a conjuring act
.
Apparatus and Materials
- Coin
- Card (such as postcard)
- Beaker
- Thread (beraking force, approx 1 N)
- Mass, large, 1 kg or more
- Retort stand, boss, and clamp
- Pile of books
- Mass, 1 g
- Blocks, wooden, with rounded edges, smooth, 5 (approx 10 cm x 7.5 cm x 5 cm)
- Hammer or mallet
- G-clamps
Health & Safety and Technical Notes
Read our standard health & safety guidance
Procedure
-
Coin and tumbler
- Place the coin on the card, and place the card over the open end of a beaker.
- Flick the card away sharply and observe the effect of the coin's motion. One large mass
- Hang a large mass (1 kg or more) by thread from a strong, rigid support. Attach a second thread to the underside of the mass.
- Pull the lower thread with a force that increases slowly until one of the threads breaks.
- Try again with a short sharp pull.
- Set up a pile of books or magazines on the bench and pull out one of the books in the middle quickly.
- Show that the thread can support a suspended mass of about 100 g.
- Tie the thread to the small mass. Hold the other end of the thread with the thread slack.
- A very abrupt jerk of the thread will break it. Pile of bricks As a reverse form of 6, push a wooden brick in to replace the bottom one at the bottom of a pile of similar wooden blocks.
- Build a pile of four blocks.
- Push a fifth brick quickly at the bottom brick of the pile. The fifth brick goes in and the bottom brick goes out. This is most dramatic if the fifth brick is projected along the table towards the pile by hitting it with a small mallet.
Teaching Notes
- Step 2: Pulling the cord slowly means the coin has a low acceleration, and so the frictional force between card and coin is big enough to accelerate the coin. Pulling the cord quickly requires too great a frictional force to accelerate the coin and so slipping occurs.
- Steps 4 and 5: Due to the weight of the mass, the upper thread breaks in the first case. But due to the inertia of the mass, the lower thread breaks in the second case. So by applying forces differently you can successfully predict which thread will break.
- Step 9: A slow pull just moves the mass along, but a quick pull snaps the thread because the force required for the high acceleration of the mass is greater than the thread's breaking strength.
- Steps 6 and 11: The only force that the moving book can exert on the pile of books above it is friction. If the acceleration of the moving books/blocks is large enough, there is insufficient force to make the pile above it move too.
- A variation is to pull a table cloth from beneath some unwanted crockery.
This experiment was safety-tested in March 2005
Up next
Balancing forces
Demonstration
The effect of friction is reduced so that you can see that a pair of balanced forces produce zero acceleration: but not necessarily zero velocity.
Apparatus and Materials
- Plank, smooth
- Rollers, 10
- Retort stands, bosses and clamps, 2
- Demonstration spring balances, 2
- Single pulleys on clamps, 4
- Masses, 1 kg, 2
- Weight hanger with slotted weights, 10 g
- Cord
Health & Safety and Technical Notes
The person standing near the additional (upper) mass to read the spring balance should be prepared to catch the retort stand should it topple over.
Read our standard health & safety guidance
Procedure
- Place the plank on the rollers and the two stands on the plank. Each stand carries one pulley fixed towards the base and a spring balance. For each one, a cord passes under the pulley and over another pulley, which you should clamp firmly to the end of the bench.
- Hang a 1-kg mass from each cord. Adjust the positions of these masses so that when one mass is on the floor the other is almost at bench height.
- Add an additional mass to the upper mass. If necessary, give the system a small push so that it moves on its rollers, and quickly reaches a constant velocity. The additional mass should be such that the plank does not continue to accelerate (50 g is usually about the right value).
Teaching Notes
- The forces applied to the system are initially equal and opposite, so that the system does not accelerate. Its velocity remains zero. The fairly small added mass is sufficient to compensate for frictional force, so that total horizontal force on the system is again zero. When this condition is achieved, the system has zero acceleration and constant velocity. Explain this.
- Whenever forces are not balanced, the system accelerates.
- This resulting motion is consistent with Newton's first law. Any object has zero acceleration (so stays still or has unchanging velocity) except when an unbalanced force acts on it. The law defines what force is: it is what causes acceleration.
This experiment was safety-tested in April 2005
Up next
Newton's first law - a demonstration
Demonstration
This shows that a body moves with constant velocity unless an unbalanced force acts on it. The constant velocity can have any value, including zero.
Apparatus and Materials
- Crank assembly
- Demonstration spring balances, 2
- Plank, short
- Steel rollers, 10
- Brick, wooden
Health & Safety and Technical Notes
Read our standard health & safety guidance
The plank should ideally be about 75 cm long.
Procedure
- Put the rollers under the plank so that it can move freely on them, with very little friction.
- Attach the plank to a G-clamp at the end of the bench, with a horizontal string to keep it from moving. Insert a spring balance, which will measure the force exerted on the plank when you drag the brick along it.
- Place the brick on the plank. Use string to connect the brick to a second spring balance and to connect that to a crank assembly.
- Drag the brick along the plank by turning the crank.
- Students watch the readings of the two spring balances to see if the two forces are equal, and match this to the type of motion, accelerated or unaccelerated, of the brick.
Teaching Notes
- Newton's first law says that a body stays at rest or moves at a constant velocity unless an unbalanced force acts on it.
- So:
- Whenever there is no net force there is no acceleration
- Whenever there is a net force there must be acceleration.
This experiment was safety-tested in March 2005
Up next
Newton's laws of motion
First and second laws
If you are considering the forces acting on just one body, either law I or law II will apply.
The first law describes what happens when the forces acting on a body are balanced (no resultant force acts) – the body remains at rest or continues to move at constant velocity (constant speed in a straight line).
If a book is placed on a table, it stays at rest. This is an example of Newton’s first law. There are two forces on the book and they happen to balance owing to the elastic properties of the table. The table is slightly squashed by the book and it exerts an elastic force upwards equal to the weight of the book. You can show this by placing a thick piece of foam rubber on a table and placing a book on top of it. The foam rubber squashes.
Galileo was the first person to challenge the common sense notion that steady motion requires a steady force. He looked beyond the obvious and was able to say if there was no friction then
an object would continue to move at constant velocity. In other words, he put forward a hypothesis. He could see that a motive force is generally needed to keep an object moving in order to balance frictional forces opposing the motion.
The motion of air molecules is a good example to consider with students. When air temperature is constant, no force is applied to keep air molecules moving, yet they do not slow down. If they did, in a matter of minutes the air would condense into a liquid.
The second law describes what happens when the forces acting on a body are unbalanced (a resultant force acts). The body changes its velocity, v, in the direction of the force, F, at a rate proportional to the force and inversely proportional to its mass, m. The rate of change of v is proportional to F / m. And rate of change of velocity is acceleration, a.
So if the table mentioned above were in an upwardly accelerated lift, an outside observer would see that the two forces acting on the book were unequal. The resultant force would be sufficient to give the book the same upward acceleration as the lift. Put some bathroom scales between the book and the table. If the book is accelerating downwards, its weight would be greater than the reaction force from the table. The book would, however, appear to be weightless.
Mass is measured in kilograms and acceleration in m /s2. With an appropriate choice of unit for force, then the constant of proportionality, k, in the equation F = k ma is 1. This is how the newton is defined, giving F = ma or a = F / m.
This can also be expressed as F = rate of change of momentum or F = Δ p / Δ t.
Newton wanted to understand what moves the planets. He realized that a planet requires no force along its orbit to move at constant speed, but it does require a force at right angles to its motion (gravitational attraction to the Sun) to constantly change direction.
The third law
Newton’s third law can be stated as ‘interactions involve pairs of forces’. Be careful in talking about third law pairs (often misleadingly called ‘action’ and ‘reaction’). Many students find this law the most difficult one to understand.
Returning to the book on a table, there are three bodies involved: the Earth, the book, and the table. In this example, the interaction pairs of forces are:
- The weight of the book and the pull of the book on the Earth (gravitational forces)
- The push of the book on the table and the push of the table on the book (contact forces)
In general, action and reaction pairs can be characterized as follows:
- They act on two different bodies
- They are equal in magnitude but opposite in direction
- They are the same type of force (e.g. gravitational, magnetic, or contact)
Up next
Mass
Mass is a difficult, strange and sophisticated concept but it is important to build up an understanding of it. Students may have been introduced to the word by teachers slowly introducing the difference between mass and weight and learning how to use the words correctly.
Experiments show that the more trolleys you pile together, the bigger the force which is needed for a given acceleration or the less acceleration we get for a standard pull. There is something about these chunks of matter that makes them difficult to accelerate; not difficult in the sense of a rough backward drag of friction but a sluggishness, a slowness to get moving. The effect of a small resultant force is slow but sure; you can get any amount of motion if you wait for it. Newton himself described mass as a ‘quantity of matter’. You could call it the amount of stuff related to the number of atoms in the object. This is inertial mass
.
The weight of an object is the pull of the Earth on that object and so it is a force. Gravitational mass is what makes a body exert and experience a gravitational force.
A useful thought experiment:
Imagine experimenters in a space ship in outer space, free from a gravitational field, trying to pull a trolley along horizontally
on a frictionless table. They use a spring to exert a pull so that the trolley accelerates. Then they hang the trolley vertically
on the same spring, holding the top of the spring in one hand. They accelerate the trolley again by pulling it upwards with the spring. For the same stretch of spring in each case what differences are noticed between the motions? [none]
By drawing ‘leading diagrams’ on the board one can mislead students temporarily into believing that vertical and horizontal have real meaning and are different. They may realize they have been tricked. The directions may be at right angles to each other, but vertical
is defined only where there is a gravitational field. Hopefully, they will be left with a feeling that mass is still there needing a force to accelerate it and gaining the same acceleration with the same force whatever the direction of the pull.
Early in the 20th Century, Einstein showed that the inertial and gravitational masses of any object are equivalent. The standard unit for mass is the kilogram. Until 2019 this was defined as the mass of a lump of metal kept in Sèvres in France. Since 2019 it has been defined in terms of the Planck constant, the speed of light and hyperfine transition frequency of 133cs (which defines the second).
Up next
Inertia
The tendency of a body to resist any change in its motion (speed or direction) – in other words, to resist any change in its acceleration – is called its ‘inertia’. Mass can be thought of as a measure of a body’s inertia.
Inertia means ‘reluctance to change’. Inertia reduces a rate of change but cannot stop it. Inertia can take many forms, e.g.
- Electromagnets have electrical inertia: they resist changes of current through their coils
- Flutes and organ pipes have acoustic inertia: their vibrations take time to diminish after the forces causing them stop
You might help students develop a feeling for inertia by asking them:
- Can you stop a moving railway carriage that is smoothly running along a line, having just been shunted? Yes, but can you stop it easily, or at once?
- What keeps a spaceship going once it is far out in space, well away from the gravitational pull of the Earth and Sun, and the rocket motors are turned off? Is there anything to stop it moving?
In both cases, inertia keeps the object moving. A force is needed to change its velocity, but even the smallest resultant (net) force will do so.
Masses of objects can be compared in principle by seeing how their velocity changes compare, in response to the same force or in the same interaction.
Up next
Galileo's thought experiment
Galileo thought that a ball, rolling or sliding down a hill without friction, would run up to the same height on an opposite hill.
Suppose that the opposite hill was horizontal. Would the ball's motion continue forever along the tangent, or forever parallel to the Earth's surface?
Galileo's conclusion from this thought experiment was that no force is needed to keep an object moving with constant velocity.
Newton took this as his first law of motion.